Fascinating. Is this documented anywhere? Potentially I would also need to do this in reverse - would love to see if Turkish has a baggage interline agreement with AA/BA to do the same.
Yes there are multiple ways of checking existing interline agreements which effectively have nothing to do with alliances (except that being in the same alliance pretty much guarantees an interline agreement, but essentially, almost all major airlines interline). However, BA's commercial policy is not to check bags through when the customer is flying on separate tickets with different airlines (there are, however, exceptions. I have benefited from some from some outstations which I won't name to avoid causing the helpful people trouble). Some other airlines are also becoming more restrictive than they used to but the majority will happily interline.
However, if you are on separate tickets, you should always allow plenty of time. As other posters mentioned, if your first flight is delayed, you are on your own and your attempt to save one or two hours could end up costing you dearly. I would always recommend at least 3 hours, more if a change of terminal and clearing immigration and waiting to pick up and recheck luggage is involved.